The prior probabilities for events A₁, A₂, and A3 are P(A₁) = 0.20, P(A₂) = 0.50, and P(A3) = 0.30. The conditional probabilities of event B given A₁, A₂, and A3 are P(B | A₁) = 0.30, P(B|A₂) = 0.50, and P(B | A₂) = 0.20. (Assume that A₁, A₂, and Aare mutually exclusive events whose union is the entire sample space.)(a) Compute P(Bn A₂), P(B n A₂), and P(B n A3).P(B n A₂) =P(Bn A₂)P(Bn A₂) =P(A)P(BIA)(b) Apply Bayes' theorem, PA, 1 B)=P(A₂)P(B | A₂) + P(A₂)P(B | A₂) + ... + P(A)P(BA)XA₂(c) Use the tabular approach to applying Bayes' theorem to compute P(A₁ | B), P(A₂ 1 B), and P(A3 | B). (Round your answers to two decimal places.)Events P(A₁) P(B|A₂) P(A, B)P(A, | B)A₁A30.200.50xXX0.301.000.300.500.20FPSIGNto compute the posterior probability P(A₂ | B). (Round your answer to two decimal places.)1.00

LetA1,A2,and A3 are mutually exclusive events and their prior probabilities are given…

The prior probabilities for events A₁, A₂, and A3 are P(A₂) = 0.20, P(A₂) = 0.50, and P(A3) = 0.30. The conditional probabilities of event B given A₁, A₂, and A3 are P(B | A₁) = 0.30, P(B|A₂) = 0.50, and P(B | A₂) = 0.20. (Assume that A₁, A₂, and A are mutually exclusive events whose union is the entire sample space.) (a) Compute P(B n A₂), P(B n A₂), and P(B n A3). x P(BnA₂) = P(Bn A₂) = X P(Bn A₂) x P(A)P(BIA) (b) Apply Bayes' theorem, PA, 1 B) = P(A₁)P(B | A₁) + P(A₂)P(B | A₂) + ... + P(A)P(B \ A₂)” A₁ - A₂ (c) Use the tabular approach to applying Bayes' theorem to compute P(A₁ | B), P(A₂ 1 B), and P(A3 | B). (Round your answers to two decimal places.) Events P(A₁) P(BA) P(A,B) P(A, IB) A3 X 0.20 0.50 0.30 1.00 0.30 0.50 C C 0.20 . CHEL SAN to compute the posterior probability P(A₂ | B). (Round your answer to two decimal places.) 1.00

The prior probabilities for events A₁, A₂, and A3 are P(A₂) = 0.20, P(A₂) = 0.50, and P(A3) = 0.30. The conditional probabilities of event B given A₁, A₂, and A3 are P(B | A₁) = 0.30, P(B|A₂) = 0.50, and P(B | A₂) = 0.20. (Assume that A₁, A₂, and A are mutually exclusive events whose union is the entire sample space.) (a) Compute P(B n A₂), P(B n A₂), and P(B n A3). x P(BnA₂) = P(Bn A₂) = X P(Bn A₂) x P(A)P(BIA) (b) Apply Bayes' theorem, PA, 1 B) = P(A₁)P(B | A₁) + P(A₂)P(B | A₂) + ... + P(A)P(B \ A₂)” A₁ - A₂ (c) Use the tabular approach to applying Bayes' theorem to compute P(A₁ | B), P(A₂ 1 B), and P(A3 | B). (Round your answers to two decimal places.) Events P(A₁) P(BA) P(A,B) P(A, IB) A3 X 0.20 0.50 0.30 1.00 0.30 0.50 C C 0.20 . CHEL SAN to compute the posterior probability P(A₂ | B). (Round your answer to two decimal places.) 1.00

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter9: Multivariable Calculus

Section9.3: Maxima And Minima

Problem 35E

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